Apparatus and method for calibrating timing mismatch of edge rotator operating on multiple phases of oscillator

ABSTRACT

An exemplary calibration apparatus for calibrating timing mismatch of an edge rotator operating on multiple phases of an oscillator includes a capturing block arranged to capture phase error samples, and a calibrating block arranged to adjust timing of said edge rotator according to said phase error samples. An exemplary calibration method for calibrating timing mismatch of an edge rotator operating on multiple phases of an oscillator includes the following steps: capturing phase error samples, and adjusting timing of said edge rotator according to said phase error samples.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. provisional application No.61/368,015, filed on Jul. 27, 2010 and incorporated herein by reference.

BACKGROUND

The disclosed embodiments of the present invention relate to generatinga clock signal, and more particularly, to a calibration apparatus forcalibrating timing mismatch of an edge rotator operating on multiplephases of an oscillator and related calibration method thereof.

With the development of the semiconductor technology, more and morefunctions are allowed to be supported by a single electronic device. Forexample, a multi-radio combo-chip product may support a plurality ofcommunication protocols. All of the radio-frequency (RF) oscillatorsshould be properly designed to avoid conflicting with each other.Specifically, good isolation is required, and injection pulling amongoscillators of different radios should be prevented. For example, thepulling of one LC-tank oscillator due to the strong harmonic of thepower amplifier (PA) output should be avoided; besides, the pulling ofone LC-tank oscillator due to a local oscillator (LO) signal or PAsignal of another integrated radio should be avoided. Thus, it resultsin a complicated frequency plan and difficult local oscillator design,especially in analog circuits. In a case where the analog approach isemployed, it requires conventional analog blocks such as frequencydivider(s) and mixer(s) which limit the frequency offset ratio to arational number, and requires an LC-tank for unwanted side-band spursuppression which inevitably consumes large area and current.

Thus, there is a need for an innovative non-harmonic clock generatordesign which may employ a digital realization for generating an outputclock having non-harmonic relationship with an input clock throughfrequency translation, and also employ an autonomous calibration processto compensate for delay mismatch of the non-harmonic clock generator.

SUMMARY

In accordance with exemplary embodiments of the present invention, acalibration apparatus for calibrating timing mismatch of an edge rotatoroperating on multiple phases of an oscillator and related calibrationmethod thereof are proposed.

According to a first aspect of the present invention, an exemplarycalibration apparatus for calibrating timing mismatch of an edge rotatoroperating on multiple phases of an oscillator is disclosed. Theexemplary calibration apparatus includes a capturing block and acalibrating block. The capturing block is arranged to capture phaseerror samples. The calibrating block is arranged to adjust timing of theedge rotator according to the phase error samples.

According to a second aspect of the present invention, an exemplarycalibration method for calibrating timing mismatch of an edge rotatoroperating on multiple phases of an oscillator is disclosed. Theexemplary calibration method includes following steps: capturing phaseerror samples; and adjusting timing of the edge rotator according to thephase error samples.

According to a third aspect of the present invention, an exemplary clockgenerating apparatus is disclosed. The exemplary clock generatingapparatus includes a clock generator and a calibration apparatus. Theclock generator includes an oscillator block, a delay circuit, and anoutput block. The oscillator block is arranged to provide a first clockof multiple phases. The delay circuit is arranged to delay at least oneof the multiple phases of the first clock to generate a second clock ofmultiple phases. The output block is arranged to receive the secondclock and generate a third clock by selecting signals from the multiplephases of the second clock. The output block includes an edge rotatoroperating on the multiple phases of the second clock, wherein the thirdclock has non-harmonic relationship with the first clock. Thecalibration apparatus is arranged to calibrate timing mismatch of theedge rotator, and includes a capturing block arranged to capture phaseerror samples, and a calibrating block arranged to adjust timing of theedge rotator according to the phase error samples.

These and other objectives of the present invention will no doubt becomeobvious to those of ordinary skill in the art after reading thefollowing detailed description of the preferred embodiment that isillustrated in the various figures and drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram illustrating a generalized clock generatoraccording to an exemplary embodiment of the present invention.

FIG. 2 is a diagram illustrating a clock generator according to a firstexemplary embodiment of the present invention.

FIG. 3 is a diagram illustrating a first clock, a second clock, amultiplexer output, a third clock, and a control signal shown in FIG. 2.

FIG. 4 is a diagram illustrating a clock generator according to a secondexemplary embodiment of the present invention.

FIG. 5 is a diagram illustrating a first clock, a second clock, a fourthclock, a first multiplexer output, a third clock, and a secondmultiplexer output shown in FIG. 4.

FIG. 6 is a diagram illustrating a clock generator according to a thirdexemplary embodiment of the present invention.

FIG. 7 is a diagram illustrating a first clock, multiplexer outputs, asecond clock, and a third clock shown in FIG. 6.

FIG. 8 is a diagram illustrating one implementation of a delay-lockedloop (DLL) based non-harmonic clock generator according to an exemplaryembodiment of the present invention.

FIG. 9 is a diagram illustrating a first clock, a second clock, amultiplexer output, and a third clock shown in FIG. 8.

FIG. 10 is a diagram illustrating another implementation of a DLL basednon-harmonic clock generator according to an exemplary embodiment of thepresent invention.

FIG. 11 is a diagram illustrating a first clock, a second clock, and athird clock shown in FIG. 10.

FIG. 12 is a diagram illustrating an all-digital phase-locked loop(ADPLL) employing a non-harmonic clock generator and with delaycalibration according to an exemplary embodiment of the presentinvention.

FIG. 13 is a diagram illustrating an exemplary delay calibrationsimulation result of a delay value set to one adjustable delay cell.

FIG. 14 is a diagram illustrating an exemplary delay calibrationsimulation result of a delay value set to another adjustable delay cell.

DETAILED DESCRIPTION

Certain terms are used throughout the description and following claimsto refer to particular components. As one skilled in the art willappreciate, manufacturers may refer to a component by different names.This document does not intend to distinguish between components thatdiffer in name but not function. In the following description and in theclaims, the terms “include” and “comprise” are used in an open-endedfashion, and thus should be interpreted to mean “include, but notlimited to . . . ”. Also, the term “couple” is intended to mean eitheran indirect or direct electrical connection. Accordingly, if one deviceis electrically connected to another device, that connection may bethrough a direct electrical connection, or through an indirectelectrical connection via other devices and connections.

In accordance with exemplary embodiment of the present invention, thefrequency translation used for generating an output clock havingnon-harmonic relationship with an input clock is realized using an edgesynthesizer based on edge selection and delay adjustment. For example,the new edge may be created by certain delay mechanism, such as a delayline or a delay-locked loop. The offset frequency may be programmable byselecting the edge transversal pattern and properly adjusting the delayvalues. Besides, the phase error/delay mismatch resulted from anincorrect delay value setting or other factor(s) may be detected andcalibrated by the proposed autonomous calibration process. The proposednon-harmonic clock generator has a flexible frequency plan for spuravoidance, and is suitable for any frequency ratio needed. Moreover, theproposed non-harmonic clock generator has a simple circuit design due tothe fact that an edge synthesizer for selection of various clock phasesis employed to replace the analog mixer of the conventional analogapproach that requires additional filtering to remove mixing spuriousproducts and consumes large current and circuit area. The proposednon-harmonic clock generator may be employed in a wireless communicationapplication, such as a multi-radio combo-chip product. However, this isnot meant to be a limitation of the present invention. Any applicationusing the proposed non-harmonic clock generator for providing an outputclock having non-harmonic relationship with an input clock falls withinthe scope of the present invention. Technical features of the proposednon-harmonic clock generator are detailed as below.

FIG. 1 is a block diagram illustrating a generalized clock generatoraccording to an exemplary embodiment of the present invention. The clockgenerator 100 includes an oscillator block 102, a delay circuit 104, andan output block 106. The oscillator block 102 is arranged to provide afirst clock CLK1 of multiple phases P₁₁, P₁₂, . . . , P_(1N). The delaycircuit 104 is coupled to the oscillator block 102, and arranged todelay at least one of the multiple phases P₁₁-P_(1N) of the first clockCLK1 to generate a second clock CLK2 of multiple phases P₂₁, P₂₂, . . ., P_(2N). The output block 106 is coupled to the delay circuit 104, andarranged to receive the second clock CLK2 and generate a third clockCLK3 by selecting signals from the multiple phases P₂₁-P_(2N) of thesecond clock CLK2. It should be noted that the third clock CLK3 hasnon-harmonic relationship with the first clock CLK1. By way of example,but not limitation, the non-harmonic relationship means clock edges ofthe third clock CLK3 are not statically aligned with that of the firstclock CLK1, or the clock frequencies of the third clock CLK3 and thefirst clock CLK1 have a non-integer ratio. With the delay circuit 104inserted between the oscillator block 102 and the output block 106 fordelaying at least one of the phases provided by the oscillator block102, desired phases needed by the output block 106 are generated. Theoscillator block 102 may be implemented by any available oscillator thatis capable of providing a multi-phase clock output. In one exemplarydesign, the oscillator block 102 may be implemented by an LC-tankoscillator core followed by an edge divider. For example, the oscillatorblock 102 can comprise an oscillator circuit producing a differentialsignal followed by a divide-by-two circuit producing a quadrature clockoutput. Alternatively, the LC-tank oscillator can be followed by one ormore delay cells. It needs to be emphasized that, in general, a delaycan be achieved either by reclocking a signal (edge division falls intothis category) or through propagation delay (delay elements, such asinverters, buffers, delay lines fall into this category). Thus, at leastone of the multiple phases of the first clock is generated by clock edgedivision or by delaying another of the multiple phases of the firstclock with a phase offset, where the phase offset is determined by arelationship between a frequency of the first clock CLK1 and a frequencyof the third clock CLK3. Further details of the clock generator 100 aredescribed as below.

Please refer to FIG. 2, which is a diagram illustrating a clockgenerator according to a first exemplary embodiment of the presentinvention. The implementation of the exemplary clock generator 200 isbased on the structure shown in FIG. 1, and therefore has an oscillatorblock 202, a delay circuit 204, and an output block 206. In thisexemplary embodiment, the oscillator block 202 is realized by anoscillator core 212 such as a digitally-controlled oscillator (DCO) witha tuning word input (not shown), and a frequency divider 214 arranged toprovide a first clock X₁ with multiple phases according to an output ofthe oscillator core 212. As shown in the figure, the first clock X₁includes quadrature clock signals I+, Q+, and I−, where the clocksignals I+ and Q+ have a 90-degree phase difference therebetween, andthe clock signals I+ and I− have a 180-degree phase differencetherebetween. It should be noted that the implementation of theoscillator block 202 is not limited to a combination of the oscillatorcore 212 and the frequency divider 214. In an alternative design, theoscillator block 202 may be implemented by the oscillator core 212 forgenerating the clock signal I+ with a period equal to T₁, and aplurality of delay cells with predetermined delay values (e.g.,

$\left( {{e.g.},{\frac{T_{1}}{4}\mspace{14mu}{and}\mspace{14mu}\frac{T_{1}}{2}}} \right)$applied to the clock signal I+ to thereby generate the clock signals Q+and I−. The same objective of providing a multi-phase clock output isachieved.

The delay circuit 204 includes a first delay cell 222 and a second delaycell 224. Supposing that the period of the first clock X₁ is T₁, thefirst delay cell 222 is arranged to apply a delay value

$\frac{T_{1}}{12}$to the incoming clock signal Q+, and the second delay cell 224 isarranged to apply a delay value

$\frac{T_{1}}{6}$to the incoming clock signal I−. Therefore, the second clock X₂ includesclock signals I+, Q+′, and I−′ with different phases.

The output block 206 includes a multiplexer 232, a toggle circuit 234,and a controller 236. The multiplexer 232 is arranged to generate amultiplexer output MUX_OUT by multiplexing the multiple phases of thesecond clock X₂ according to a control signal SC. The controller 236 isarranged to receive the multiplexer output MUX_OUT and generate thecontrol signal SC according to the multiplexer output MUX_OUT. Forexample, the controller 236 in this exemplary embodiment may beimplemented by a modulo-3 counter. Therefore, due to the counter valuesequence produced by the modulo-3 counter as the control signal SC, themultiplexer 232 would output the clock signals I+, Q+′, and I−′ as itsoutput, cyclically. The toggle circuit 234 is arranged to receive themultiplexer output MUX_OUT and generate a third clock X₃ according tothe multiplexer output MUX_OUT. More specifically, the third clock X₃ istoggled (i.e., change its output logic level from “0” to “1” or viceversa) when the toggle circuit 234 is triggered by the multiplexeroutput MUX_OUT. For example, the toggle circuit 234 may be implementedby a T flip-flop which is triggered by rising edges of the multiplexeroutput MUX_OUT.

Please refer to FIG. 3 in conjunction with FIG. 2. FIG. 3 is a diagramillustrating the first clock X₁, the second clock X₂, the multiplexeroutput MUX_OUT, the third clock X₃, and the control signal SC. As can beseen from FIG. 3, there is a phase difference between the clock signalsQ+ and Q+′ due to the intentionally applied delay value

$\frac{T_{1}}{12},$and there is a phase difference between the clock signals I− and I−′ dueto the intentionally applied delay value

$\frac{T_{1}}{6}.$At time t₁, the control signal SC is updated to a counter value “1” dueto the rising edge of the clock signal I+. Therefore, the multiplexer232 outputs the clock signal Q+′ as the multiplexer output MUX_OUT. Attime t2, the clock signal Q+′ has a rising edge which triggers both ofthe toggle circuit 234 and the controller 236. Therefore, the thirdclock X₃ has a transition from a low logic level “0” to a high logiclevel “1”, and the control signal SC is updated by a counter value “2”.As a result, the multiplexer 232 outputs the clock signal I−′ as themultiplexer output MUX_OUT. At time t₃, the clock signal I−′ has arising edge which triggers both the toggle circuit 234 and thecontroller 236. Therefore, the third clock X₃ has a transition from thehigh logic level “1” to the low logic level “0”, and the control signalSC is updated by a counter value “0”. As a result, the multiplexer 232outputs the clock signal I+ as the multiplexer output MUX_OUT. As thefollowing operation can be easily deduced by analogy, furtherdescription is omitted here for brevity. Considering a case where thefrequency of the first clock X₁ is 1666.7 MHz (i.e., T₁=600 ps), thefrequency of the generated third clock X₃ would be 2500.0 MHz (i.e.,T₃=400 ps). To put it another way, the delay-line based non-harmonicclock generator shown in FIG. 2 is capable of making the frequencies ofthe input clock (e.g., first clock X₁) and the output clock (e.g., thirdclock X₃) have a non-integer ratio equal to 2/3.

As shown in FIG. 2 and FIG. 3, when switching between two clock signalsfed into the multiplexer 232 occurs, a transition from one logic levelto another logic level occurs due to the clock signals having differentlogic levels, which may result in a switching glitch in the multiplexeroutput MUX_OUT under certain condition. To avoid this switching glitchissue, the present invention therefore proposes a modified non-harmonicclock generator with a multiplexer which is controlled to switch fromone clock signal to another clock signal when the clock signals bothhave the same logic level. Please refer to FIG. 4, which is a diagramillustrating a clock generator according to a second exemplaryembodiment of the present invention. The implementation of the exemplaryclock generator 400 is also based on the structure shown in FIG. 1, andtherefore has an oscillator block 402, a delay circuit 404, and anoutput block 406. The oscillator block 402 is arranged to generate afirst clock X₁ including clock signals I+ and I− that have a 180-degreephase difference therebetween. The delay circuit 404 includes a firstdelay unit 412 and a second delay unit 414, wherein the first delay unit412 has delay cells 413_1 and 413_2 included therein, and the seconddelay unit 414 has delay cells 415_1 and 415_2 included therein. Thefirst delay unit 412 is arranged to delay the multiple phases (e.g.,differential phases) of the first clock X₁. In this exemplaryembodiment, each of the delay cells 413_1 and 413_2 is employed to applya delay value T₂ to the incoming clock signal. Accordingly, the firstdelay unit 412 outputs clock signals I+′ and I—′ to the following signalprocessing stage (i.e., the second delay unit 414).

The second delay unit 414 is arranged to delay at least one of themultiple delayed phases generated from the first delay unit 412. In thisexemplary embodiment, each of the delay cells 415_1 and 415_2 isemployed to apply a delay value

$\frac{T_{1}}{4}$to an incoming clock signal. Accordingly, the second delay unit 414outputs a second clock X₂ including clock signals A, B, C, D withdifferent phases. As can be seen from FIG. 4, the multiple phases of thesecond clock X₂ include delayed phases (e.g., clock signals B and D)generated from delay cells 415_1, 415_2 of the second delay unit 414 anddelayed phases (e.g., clock signals A and C) generated from delay cells413_1, 413_2 of the first delay unit 412.

The output block 406 is arranged to control selection of the multiplephases of the second clock X₂ by referring to at least the multiplephases of the first clock X₁. As shown in FIG. 4, the output block 406includes a first multiplexer 422, a toggle circuit 424, and a controller426. The first multiplexer 422 is arranged to generate a firstmultiplexer output MUX_OUT1 by multiplexing the multiple phases of thesecond clock X₂ according to a first control signal SC1. The togglecircuit 424 is arranged to receive the first multiplexer output MUX_OUT1and generate a third clock X₃ according to the first multiplexer outputMUX_OUT1. More specifically, the third clock X₃ is toggled when thetoggle circuit 424 is triggered by the first multiplexer outputMUX_OUT1. For example, the toggle circuit 424 may be implemented by a Tflip-flop which is triggered by rising edges of the first multiplexeroutput MUX_OUT1.

In this exemplary embodiment, the controller 426 is arranged to receivethe first multiplexer output MUX_OUT1 and the multiple phases of thefirst clock X₁, and generate the first control signal SC1. As shown inFIG. 4, the controller 426 includes a third delay unit 432, a secondmultiplexer 434, a first control unit 436, and a second control unit438. The third delay unit 432 is arranged to delay at least one of themultiple phases of the first clock X₁. In this exemplary embodiment, thethird delay unit 432 includes delay cells 433_1 and 433_2 each applyinga delay value

$\frac{T_{1}}{4}$to an incoming clock signal. Therefore, the third delay unit 432 outputsa fourth clock X₄ including clock signals A′, B′, C′, D′ with differentphases. The second multiplexer 434 is arranged to generate a secondmultiplexer output MUX_OUT2 by multiplexing the multiple phases of thefourth clock X₄ according to a second control signal SC2, wherein themultiple phases received by the second multiplexer 434 include delayedphases (e.g., clock signals B′ and D′) generated from delay cells 433_1,433_2 of the third delay unit 432 and the multiple phases (e.g., A′ andC′) of the first clock X₁.

The first control unit 436 is arranged to receive the second multiplexeroutput MUX_OUT2 and accordingly generate the first control signal SC1 tothe first multiplexer 422. Similarly, the second control unit 438 isarranged to receive the first multiplexer output MUX_OUT1 andaccordingly generate the second control signal SC2 to the secondmultiplexer 434. For example, the first control unit 436 and the secondcontrol unit 438 may be implemented by modulo-4 counters, which outputcounter values as the desired control signals.

Please refer to FIG. 5 in conjunction with FIG. 4. FIG. 5 is a diagramillustrating the first clock X₁, the second clock X₂, the fourth clockX₄, the first multiplexer output MUX_OUT1, the third clock X₃, and thesecond multiplexer output MUX_OUT2. As can be seen from FIG. 5, there isa phase difference between the clock signals I+ and A due to theintentionally applied delay value T₂, there is a phase differencebetween the clock signals I+ and B due to the intentionally applieddelay value

${T_{2} + \frac{T_{1}}{4}},$there is a phase difference between the clock signals I− and C due tothe intentionally applied delay value T₂, and there is a phasedifference between the clock signals I− and D due to the intentionallyapplied delay value

$T_{2} + {\frac{T_{1}}{4}.}$Regarding the fourth clock X₄, the clock signal A′ is the same as theclock signal I+, and the clock signal C′ is the same as the clock signalI−; however, there is a phase difference between the clock signals A′and B′ due to the intentionally applied delay value

$\frac{T_{1}}{4},$and there is a phase difference between the clock signals C′ and D′ dueto the intentionally applied delay value

$\frac{T_{1}}{4}.$

Suppose that the first control signal SC1 is initialized by a countervalue “0”, and the second control signal SC2 is initialized by a countervalue “0”. Thus, before time t₁, the first multiplexer 422 outputs theclock signal A as the first multiplexer output MUX_OUT1, and the secondmultiplexer 434 outputs the clock signal D′ as the second multiplexeroutput MUX_OUT2. At time t₁, the second control unit 438 and the togglecircuit 424 are both triggered by the rising edge of the clock signal A.Therefore, the third clock X₃ has a transition from a low logic level“0” to a high logic level “1”, and the second control signal SC2 isupdated by a counter value “1”. Therefore, the second multiplexer 434now outputs the clock signal A′ as the second multiplexer outputMUX_OUT2. Please note that both of the clock signals D′ and A′ have thesame logic level “1” at the multiplexer switching timing (i.e., t₁) suchthat the unwanted switching glitch is avoided.

At time t₂, the first control unit 436 is triggered by the rising edgeof the clock signal A′. Therefore, the first control signal SC1 isupdated by a counter value “1”, and the first multiplexer 422 nowoutputs the clock signal B as the first multiplexer output MUX_OUT1.Please note that both of the clock signals A and B have the same logiclevel “0” at the multiplexer switching timing (i.e., t₂) such that theunwanted switching glitch is avoided. At time t₃, the second controlunit 438 and the toggle circuit 424 are both triggered by the risingedge of the clock signal B. Therefore, the third clock X₃ has atransition from the high logic level “1” to the low logic level “0”, andthe second control signal SC2 is updated by a counter value “2”. Thesecond multiplexer 434 now outputs the clock signal B′ as the secondmultiplexer output MUX_OUT2. Please note that both of the clock signalsA′ and B′ have the same logic level “1” at the multiplexer switchingtiming (i.e., t₃) such that the unwanted switching glitch is avoided. Asthe following operation can be easily deduced by analogy, furtherdescription is omitted here for brevity.

As can be seen from FIG. 5, the delay-line based non-harmonic clockgenerator shown in FIG. 4 is capable of making the frequencies of theinput clock (e.g., the first clock X₁) and the output clock (e.g., thethird clock X₃) to be a non-integer ratio equal to 5/2. It should benoted that τ₂<T₁, and the value of τ₂ may comfortably separate thetiming of the first and second control units 436 and 438. As the firstmultiplexer output MUX_OUT1 of the first multiplexer 422 is used tocontrol the input selection of the second multiplexer 434 and the secondmultiplexer output MUX_OUT2 of the second multiplexer 434 is used tocontrol the input selection of the first multiplexer 422, the switchingglitch issue is solved.

The clock generator configuration shown in FIG. 4 is capable of avoidingoccurrence of the switching glitch. However, this is for illustrativepurposes only, and is not meant to be a limitation of the presentinvention. Using other clock generator configuration to solve theswitching glitch issue is also feasible. Please refer to FIG. 6, whichis a diagram illustrating a clock generator according to a thirdexemplary embodiment of the present invention. The implementation of theexemplary clock generator 600 is also based on the structure shown inFIG. 1, and therefore has an oscillator block 602, a delay circuit 604,and an output block 606. In this exemplary embodiment, the oscillatorblock 602 is realized by an oscillator core (e.g., a DCO) 612, afrequency divider 614, and a swapping circuit 616. The frequency divider614, which could be realized as an edge divider, is arranged to providea first clock X₁ with multiple (e.g., quadrature) phases according to anoutput of the oscillator core 612. As shown in the figure, the firstclock X₁ includes clock signals I+, Q+, I−, and Q−, where the clocksignals I+ and Q+ have a 90-degree phase difference therebetween, theclock signals I− and Q− have a 90-degree phase difference therebetween,the clock signals I+ and I− have a 180-degree phase differencetherebetween, and the clock signals Q+ and Q− have a 180-degree phasedifference therebetween.

The swapping circuit 616 is arranged to output selected phases byalternately selecting a first set of phases from the multiple phases ofthe first clock X₁ and a second set of phases from the multiple phasesof the first clock X₁. In this exemplary embodiment, the swappingcircuit 616 includes a toggle circuit 617 and a plurality ofmultiplexers 618 and 619. The toggle circuit 617 may be implemented by aT flip-flop, which is triggered by rising edges of the clock signal I+.Therefore, during one period of the clock signal I+, the multiplexers618 and 619 output selected phases by selecting the clock signals I+ andQ+ as respective multiplexer outputs I and Q, and during another periodof the clock signal I+, the multiplexers 618 and 619 update the selectedphases by selecting the clock signals I− and Q− as respectivemultiplexer outputs I and Q.

The swapping circuit 616 outputs the selected phases of the multiplephases of the first clock X₁ to the following delay circuit 604. In thisexemplary embodiment, the delay circuit 604 includes a first delay cell622 and a second delay cell 624. Supposing that the period of the firstclock X₁ is T₁, the first delay cell 622 is arranged to apply a delayvalue

$\frac{T_{1}}{6}$to the incoming multiplexer output I, and the second delay cell 624 isarranged to apply a delay value

$\frac{T_{1}}{12}$to the incoming multiplexer output Q. As shown in FIG. 6, the secondclock X₂ includes clock signals I, I′, and Q′ with different phases.

The output block 606 includes a multiplexer 632 and a controller 636.The multiplexer 632 is arranged to generate a third clock X₃ bymultiplexing the multiple phases of the second clock X₂ according to acontrol signal SC. The controller 636 is arranged to receive the thirdclock X₃ and generate the control signal SC according to the third clockX₃. For example, the controller 636 in this exemplary embodiment may beimplemented by a modulo-3 counter. Therefore, due to the counter valuesequence produced from the modulo-3 counter, the multiplexer 632 wouldoutput the clock signals Q′, I′, and I as its output, cyclically.

Please refer to FIG. 7 in conjunction with FIG. 6. FIG. 7 is a diagramillustrating the first clock X₁, the multiplexer outputs I and Q, thesecond clock X₂, and the third clock X₃. As can be seen from FIG. 7, themultiplexer output I is set by the clock signals I− and I+, alternately;and the multiplexer output Q is set by the clock signals Q− and Q+,alternately. Besides, there is a phase difference between the clocksignals Q and Q′ due to the intentionally applied delay value

$\frac{T_{1}}{12},$and there is a phase difference between the clock signals I and I′ dueto the intentionally applied delay value

$\frac{T_{1}}{6}.$The controller 636 may be a modulo-3 counter triggered by rising edgesof the third clock X₃. Thus, the multiplexer 632 outputs the clocksignals Q′, I′ and I, cyclically.

Initially, the multiplexers 618 and 619 output clock signals I+ and Q+,respectively; and the multiplexer 632 outputs the clock signal Q′ as thethird clock X₃ due to the control signal SC set by a counter value “0”.At time t₁, the toggle circuit 617 is triggered by the rising edge ofthe clock signal I+. Therefore, the multiplexers 618 and 619 outputclock signals I− and Q−, respectively. At time t₂, the third clock X₃has a transition from the low logic level “0” to the high logic level“1”, and the controller 636 is triggered by the rising edge of the clocksignal Q′. Therefore, the control signal SC is updated by a countervalue “1”. Accordingly, the clock signal I′ is selected by themultiplexer 632 to act as its output. As shown in FIG. 7, both of theclock signals Q′ and I′ have the same logic level “1” at the multiplexerswitching timing (i.e., just after t₂) such that the unwanted switchingglitch is avoided. At time t₃, the third clock X₃ has a transition fromthe low logic level “0” to the high logic level “1”, and the controller636 is triggered by the rising edge of the clock signal I′. Therefore,the control signal SC is updated by a counter value “2”. Accordingly,the clock signal I is selected by the multiplexer 632 to act as itsoutput. As shown in FIG. 7, both of the clock signals I′ and I have thesame logic level “1” at the multiplexer switching timing (i.e., justafter t₃) such that the unwanted switching glitch is avoided. As thefollowing operation can be easily deduced by analogy, furtherdescription is omitted here for brevity.

As can be seen from FIG. 7, the delay-line based non-harmonic clockgenerator shown in FIG. 6 is capable of making the frequencies of theinput clock (e.g., the first clock X₁) and the output clock (e.g., thethird clock X₃) have a non-integer ratio equal to 2/3 which is differentfrom that of the aforementioned clock generators 200 and 400. In otherwords, with a proper design of the clock generator, any non-integerratio of input clock's frequency to output clock's frequency can berealized.

In above exemplary embodiments, various designs of a delay-line basednon-harmonic clock generator for generating an output clock havingnon-harmonic relationship with an input clock are proposed. However,this is for illustrative purposes only, and is not meant to be alimitation of the present invention. That is, using other clockgenerator configurations for generating an output clock havingnon-harmonic relationship with an input clock is feasible. Please referto FIG. 8, which is a diagram illustrating one implementation of adelay-locked loop (DLL) based non-harmonic clock generator according toan exemplary embodiment of the present invention. The clock generator800 includes an oscillator circuit 812, a delay circuit (e.g., a DLL814) that uniformly interpolates between the oscillator circuit edges,and an output block 804. Note, the oscillator circuit 812 and delaycircuit 814 can be conveniently arranged to form anoscillator/interpolator block 802. The oscillator/interpolator block 802is arranged to provide a second clock X₂ of multiple phases. In thisexemplary embodiment, the second clock X₂ includes clock signals A, B,and C with different phases. As shown in FIG. 8, theoscillator/interpolator block 802 includes the oscillator circuit (e.g.,a DCO) 812 arranged to provide a first clock X₁, and the DLL 814arranged to generate the second clock X₂ according to the first clockX₁. The DLL 814 includes a plurality of delay elements 815_1, 815_2, and815_3, and a phase detector (PD) 816 arranged to compare the phase ofone DLL output (e.g., the clock signal A) to the input clock (e.g., thefirst clock X₁) to generate an error signal which is then fed back asthe control to all of the delay elements 815_1-815_3. Please note thatthe number of delay elements implemented in the DLL 814 is adjustable,depending upon the actual design requirement/consideration. As a personskilled in the art should readily understand details of the DLL 814,further description is omitted here for brevity.

The output block 804 is arranged to receive the second clock X₂ andgenerate a third clock X₃ by selecting signals from the multiple phasesof the second clock X₂. It should be noted that the third clock X₃ hasnon-harmonic relationship with the first clock X₁. In this exemplaryembodiment, the output block 804 includes a multiplexer 822, acontroller 824, and a toggle circuit 826. The multiplexer 822 isarranged to generate a multiplexer output MUX_OUT by multiplexing themultiple phases of the second clock X₂ according to a control signal SC.The controller 824 is arranged to receive the multiplexer output MUX_OUTand generate the control signal SC according to the multiplexer outputMUX_OUT. The toggle circuit 826 is arranged to receive the multiplexeroutput MUX_OUT and generate the third clock X₃ according to themultiplexer output MUX_OUT. More specifically, the third clock X₃ istoggled when the toggle circuit 826 is triggered by the multiplexeroutput MUX_OUT. For example, the toggle circuit 826 may be implementedby a T flip-flop which is triggered by rising edges of the multiplexeroutput MUX_OUT. Note that the toggle circuit can conveniently includecircuitry to generate multiple phases of its output clock.

Please refer to FIG. 9 in conjunction with FIG. 8. FIG. 9 is a diagramillustrating the first clock X₁, the second clock X₂, the multiplexeroutput MUX_OUT, and the third clock X₃. As shown in the figure, themultiplexer output MUX_OUT is cyclically set by the clock signals A, B,and C under the control of the controller (e.g., a modulo-3 counter)824. As a person skilled in the art can readily understand thegeneration of the third clock X₃ shown in FIG. 9 after reading aboveparagraphs directed to FIG. 3, further description is omitted here forbrevity. Considering a case where the frequency of the first clock X₁ is3.2 GHz, the frequency of the generated third clock X₃ would be 2.4 GHz.To put it another way, the DLL based non-harmonic clock generator shownin FIG. 8 is capable of making the frequencies of the input clock (e.g.,the first clock X₁) and the output clock (e.g., the third clock X₃) havea non-integer ratio equal to 4/3.

Please refer to FIG. 10, which is a diagram illustrating anotherimplementation of a DLL based non-harmonic clock generator according toan exemplary embodiment of the present invention. The clock generator1000 includes an oscillator circuit 1012, a delay circuit (e.g., a DLL1014) that generates multiple edges through interpolation of its inputclock, and an output block 1004. The oscillator block 1012 and the delaycircuit (e.g., the DLL 1014) are conveniently combined into a singleoscillator/interpolator block 1002. The oscillator/interpolator block1002 is arranged to provide a second clock X₂ of multiple phases. Inthis exemplary embodiment, the second clock X₂ includes clock signals A,˜A, B, ˜B, C, and ˜C with different phases. More specifically, the clocksignals A and ˜A are out of phase, the clock signals B and ˜B are out ofphase, and the clock signals C and ˜C are out of phase. As shown in thefigure, the oscillator/interpolator block 1003 includes the oscillatorcircuit (e.g., a DCO) 1012 arranged to provide a first clock X₁including clock signals I+ and I− that are out of phase (i.e., 108degrees apart), and the DLL 1014 arranged to generate (throughinterpolation) the aforementioned second clock X₂ according to the firstclock X₁, wherein the DLL 1014 includes a plurality of delay elements1015_1, 1015_2, and 1015_3, and a phase detector (PD) 1016 arranged tocompare the phase of one DLL output (e.g., the clock signal C) to theinput clock (e.g., the clock signal I+) to generate an error signalwhich is then fed back as the control to all of the delay elements1015_1-1015_3. As a person skilled in the art should readily understanddetails of the DLL 1014, further description is omitted here forbrevity.

The output block 1004 is arranged to receive the second clock X₂ andgenerate a third clock X₃ by selecting signals from the multiple phasesof the second clock X₂. It should be noted that the third clock X₃ hasnon-harmonic relationship with the first clock X₁. In this exemplaryembodiment, the output block 1004 includes a multiplexer 1022 and acontroller 1024. The multiplexer 1022 is arranged to generate the thirdclock X₃ by multiplexing the multiple phases of the second clock X₂according to a control signal SC. The controller 1024 is arranged toreceive the first clock X₁ and generate the control signal SC accordingto the first clock X₁. For example, the controller 1024 updates thecontrol signal SC at rising edges of the clock signals I+ and I−.

Please refer to FIG. 11 in conjunction with FIG. 10. FIG. 11 is adiagram illustrating the first clock X₁, the second clock X₂, and thethird clock X₃. As shown in the figure, the multiplexer output (i.e.,the third clock X₃) is cyclically set by the clock signals A, A, ˜C, B,˜A, ˜A, C, and ˜B under the control of the controller 1024. As a personskilled in the art can readily understand the generation of the thirdclock X₃ shown in FIG. 11 after reading above paragraphs, furtherdescription is omitted here for brevity. Considering a case where thefrequency of the first clock X₁ is 3.2 GHz, the frequency of thegenerated third clock X₃ would be 2.4 GHz. To put it another way, theDLL based non-harmonic clock generator shown in FIG. 8 is capable ofmaking the frequencies of the input clock (e.g., the first clock X₁) andthe output clock (e.g., the third clock X₃) have a non-integer ratioequal to 4/3.

As mentioned above, the intentionally applied delay values are used tocreate the desired phases/edges needed by the following output block.However, the clock signals to be multiplexed may have phase errors whichwould affect the actual waveform of the output clock generated from theexemplary non-harmonic clock generator proposed in the presentinvention. Thus, there is a need for calibrating the delay values tocompensate for the delay mismatch. Please refer to FIG. 12, which is adiagram illustrating an all-digital phase-locked loop (ADPLL) employinga non-harmonic clock generator and with delay calibration according toan exemplary embodiment of the present invention. The ADPLL 1200 withdelay calibration includes a digital phase detector 1202, a digital loopfilter 1204, a delay-line based non-harmonic clock generator 1206, acalibration apparatus 1208, and a D flip-flop (DFF) 1210. For clarityand simplicity, only the components pertinent to the technical featuresof the present invention are shown in FIG. 12. That is, in anotherexemplary embodiment, the ADPLL 1200 may have additional componentsincluded therein. The general ADPLL architecture is well known in theart.

By way of example, but not limitation, the delay-line based non-harmonicclock generator 1206 may be implemented using the configuration shown inFIG. 2. Therefore, the delay-line based non-harmonic clock generator1206 includes an oscillator block 1212 and an edge synthesizer 1214having an edge rotator 1216 and a toggle circuit 1218, wherein the edgerotator 1216 includes a plurality of adjustable delay cells 1221 and1222 controlled by calibration signals ADJ_1 and ADJ_2, a multiplexer1223, and a controller (e.g., a modulo-3 counter) 1224. As a personskilled in the art can readily understand the operation of thedelay-line based non-harmonic clock generator 1206 after reading aboveparagraphs directed to the clock generator 200 shown in FIG. 2, furtherdescription is omitted here for brevity.

The DFF 1210 is implemented for generating a clock signal CKR used byinternal components of the ADPLL 1200 according to a frequency f_(R) ofa clock reference FREF and a frequency f_(V)′ of a feedback clock CKV′.The digital PD 1202 outputs phase error samples derived from a variablephase corresponding to an output of the edge rotator 1216 and areference phase. For example, the reference phase is derived from thechannel frequency command word (FCW) and the clock reference FREF fedinto the digital PD 1202, and the variable phase is derived from thefeedback clock CKV′ and the clock reference FREF fed into the digital PD1202. The digital loop filter 1204 refers to the phase error samplesgenerated from the digital PD 1202 to generate a tuning word signal tothe oscillator block 1212, which may have a DCO included therein. As aperson skilled in the art should readily understand details of thedigital PD 1202, the digital loop filter 1204, and the DFF 1210, furtherdescription is omitted here for brevity.

The calibration apparatus 1208 is implemented for calibrating timingmismatch of the edge rotator 1216 operating on multiple phases of anoscillator (e.g., the oscillator block 1212, which may be implemented bya combination of an oscillator core and a frequency divider or acombination of an oscillator core and delay cells). The calibrationapparatus 1208 includes a capturing block 1232 and a calibrating block1234. The capturing block 1232 is arranged to capture phase errorsamples generated by the digital PD 1202. The calibrating block 1234 isarranged to adjust timing of the edge rotator 1216 by generating thecalibration signal ADJ_1/ADJ_2 to the adjustable delay cell 1221/1222according to the phase error samples. It should be noted that the ADPLLmight need to be configured to operate under restricted FCW values. Moreparticularly, the fractional part of FCW value needs to correspond to aninverse of the period of the edge rotator. For example, the multiplexer1223 has three inputs and its rotational period is three. Hence, thefractional value of FCW should be ⅓ or ⅔.

In this exemplary embodiment, the capturing block 1232 includes aselector 1242, a demultiplexer (DEMUX) 1244, and a storage 1245. Thenumber of phase error samples to be captured is equal to periodicity ofthe edge rotator 1216. For example, the multiplexer 1223 selects a clockinput with no delay value intentionally applied thereto, a clock inputwith a first delay value intentionally applied thereto, and a clockinput with a first delay value intentionally applied thereto,cyclically. As the switching sequence of the multiplexer 1223 is knownbeforehand, the occurrence of the phase error samples generated from thedigital PD 1202 is predictable. Based on such an observation, when thecontrol signal SC is set by a counter value “0”, the selector 1242controls the DEMUX 1244 to store a current phase error sample P0corresponding to the clock input with no delay value applied theretointo the storage 1245; when the control signal SC is set by a countervalue “1”, the selector 1242 controls the DEMUX 1244 to store a currentphase error sample P1 corresponding to the clock input with the firstdelay value intentionally applied thereto into the storage 1245; andwhen the control signal SC is set by a counter value “2”, the selector1242 controls the DEMUX 1244 to store a current phase error sample P2corresponding to the clock input with the second delay valueintentionally applied thereto into the storage 1245.

Regarding the calibrating block 1234, it includes a calculating circuit1247 and an adjusting circuit 1248. The calculating circuit 1247 isarranged to estimate the timing mismatch of the edge rotator 1216according to the phase error samples buffered in the storage 1245, andhas a plurality of subtractors 1246_1 and 1246_2 implemented forestimating phase errors. As the clock input with no delay valueintentionally applied thereto may be regarded as a clock input having acorrect delay value, the phase error sample P0 may serve as an idealone. Thus, the subtractor 1246_1 calculates a difference between thephase error samples P1 and P0 to represent a phase error of the clockinput with the first delay value intentionally applied thereto, and thesubtractor 1246_2 calculates a difference between the phase errorsamples P2 and P0 to represent a phase error of the clock input with thesecond delay value intentionally applied thereto. To put it another way,the calculating circuit 1247 estimates the timing mismatch of the edgerotator 1216 by calculating a difference between a phase error sample(e.g., P0) of the phase error samples and each of remaining phase errorsamples (e.g., P1 and P2).

The adjusting circuit 1248 is arranged to adjust the timing of the edgerotator 1216 according to an output of the calculating circuit 1247.More specifically, the adjusting circuit 1248 controls the adjustabledelay cells 1221 and 1222 to adjust the delay values by generating thecalibrating signals ADJ_1 and ADJ_2 to the adjustable delay cells 1221and 1222. Please note that the calibrating signal ADJ_1/ADJ_2 generatedfrom the adjusting circuit 1248 does not change the delay value set tothe adjustable delay cell 1221/1222 when the estimated phase error iszero or negligible. Moreover, the adjusting circuit 1248 may be equippedwith accumulation functionality and follow a least mean square (LMS) orsteepest descent algorithm, which is generally well known in the art.Thus, the estimated phase errors generated from the subtractor 1246_1are accumulated to alleviate the noise interference, and an accumulatedphase error is referenced for controlling the calibration signal ADJ_1.Similarly, the estimated phase errors generated from the subtractor1246_2 are also accumulated to alleviate the noise interference, and anaccumulated phase error is referenced for controlling the calibrationsignal ADJ_2. This also obeys the spirit of the present invention.

In a case where the clock signal I+ generated from the oscillator block1212 may have no phase error presented therein, the correspondingcaptured phase error sample may equal zero. Therefore, the calculatingcircuit 1247 may be omitted, and the adjusting circuit 1248 directlyrefers to the phase error samples P1 and P2 to set the calibrationsignals ADJ_1 and ADJ_2. This alternative design also falls within thescope of the present invention.

The calibrating block 1208 does not stop adjusting/calibrating the delayvalue(s) until the phase errors are found negligible. As the delaycalibration is based on the actually captured phase error samples ratherthan predicted phase errors, the calibrating block 1208 thereforestochastically reduces the timing mismatch of the edge rotator 1216through the adaptive delay mismatch calibration, as shown in FIG. 13 andFIG. 14 illustrating exemplary delay calibration simulation results ofdelay values respectively set to the adjustable delay cells 1222 and1221. In the exemplary delay calibrations shown in FIG. 13 and FIG. 14,an offseted frequency is 2451*( 4/3) MHz, a central frequency is 2451MHz, and a reference clock frequency is 26 MHz. Thus, the FCW value maybe set by 125.6667, where an integer part (i.e., 125) is derived from afloor value of 2451*( 4/3)/26 (i.e., └2451*( 4/3)/26┘=125), and afractional part (i.e., 0.6667) is derived from ⅔.

Please note that the proposed autonomous calibration mechanism is notlimited to the ADPLL application. For example, the autonomouscalibration mechanism may be implemented in any PLL application whichemploys the proposed clock generator (e.g., the delay-line basednon-harmonic clock generator 1206) as long as the phase errorinformation generated from the phase detector of the PLL circuit isavailable to the calibration apparatus.

Those skilled in the art will readily observe that numerousmodifications and alterations of the device and method may be made whileretaining the teachings of the invention. Accordingly, the abovedisclosure should be construed as limited only by the metes and boundsof the appended claims.

What is claimed is:
 1. A calibration apparatus for calibrating timingmismatch of an edge rotator operating on multiple phases of anoscillator, comprising: a capturing block, arranged to capture phaseerror samples; and a calibrating block, arranged to adjust timing ofsaid edge rotator according to said phase error samples; wherein saidphase error samples are derived from a reference phase and a variablephase corresponding to an output of said edge rotator; and wherein saidreference phase is derived from a channel frequency command word (FCW)and a clock reference fed into a digital phase detector, and afractional part of an FCW value is an inverse of a period of said edgerotator.
 2. A calibration apparatus for calibrating timing mismatch ofan edge rotator operating on multiple phases of an oscillator,comprising: a capturing block, arranged to capture phase error samples;and a calibrating block, arranged to adjust timing of said edge rotatoraccording to said phase error samples; wherein said calibrating blockcomprises: a calculating circuit, arranged to estimate the timingmismatch of said edge rotator according to said phase error samples; andan adjusting circuit, arranged to adjust said timing of said edgerotator according to an output of said calculating circuit.
 3. Thecalibration apparatus of claim 2, wherein said phase error samples arederived from a reference phase and a variable phase corresponding to anoutput of said edge rotator.
 4. The calibration apparatus of claim 3,wherein said reference phase is derived from a channel frequency commandword (FCW) and a clock reference fed into a digital phase detector, anda fractional part of an FCW value is an inverse of a period of said edgerotator.
 5. The calibration apparatus of claim 2, wherein saidcalculating circuit estimates said timing mismatch of said edge rotatorby calculating a difference between a phase error sample of said phaseerror samples and each of remaining phase error samples.
 6. Thecalibration apparatus of claim 2, wherein said adjusting circuit isarranged to have accumulation functionality and follow a least meansquare (LMS) algorithm to process said output of said calculatingcircuit.
 7. The calibration apparatus of claim 2, wherein a number ofsaid phase error samples is equal to periodicity of said edge rotator.8. The calibration apparatus of claim 2, wherein said calibrating blockstochastically reduces said timing mismatch of said edge rotator.
 9. Acalibration method for calibrating timing mismatch of an edge rotatoroperating on multiple phases of an oscillator, comprising: capturingphase error samples; and adjusting timing of said edge rotator accordingto said phase error samples; wherein said step of adjusting timing ofsaid edge rotator comprises: estimating the timing mismatch of said edgerotator according to said phase error samples; wherein said timing ofsaid edge rotator is adjusted according to an output of estimating thetiming mismatch.
 10. The calibration method of claim 9, wherein saidphase error samples are derived from a reference phase and a variablephase corresponding to an output of said edge rotator.
 11. Thecalibration method of claim 10, wherein said reference phase is derivedfrom a channel frequency command word (FCW) and a clock reference fedinto a digital phase detector, and a fractional part of an FCW value isan inverse of a period of said edge rotator.
 12. The calibration methodof claim 9, wherein said step of estimating the timing mismatchcomprises: calculating a difference between a phase error sample of saidphase error samples and each of remaining phase error samples.
 13. Thecalibration method of claim 9, wherein said step of adjusting timing ofsaid edge rotator further comprises: performing accumulation upon saidoutput of said calculating circuit by following a least mean square(LMS) algorithm.
 14. The calibration method of claim 9, wherein a numberof said phase error samples is equal to periodicity of said edgerotator.
 15. The calibration method of claim 9, wherein said step ofadjusting timing of said edge rotator stochastically reduces said timingmismatch of said edge rotator.
 16. A clock generating apparatus,comprising: a clock generator, comprising: an oscillator block, arrangedto provide a first clock of multiple phases; a delay circuit, arrangedto delay at least one of said multiple phases of said first clock togenerate a second clock of multiple phases; and an output block,arranged to receive said second clock and generate a third clock byselecting signals from said multiple phases of said second clock, saidoutput block comprising: an edge rotator operating on said multiplephases of said second clock, wherein said third clock has non-harmonicrelationship with said first clock; and a calibration apparatus,arranged to calibrate timing mismatch of the edge rotator, saidcalibration apparatus comprising: a capturing block, arranged to capturephase error samples; and a calibrating block, arranged to adjust timingof said edge rotator according to said phase error samples; wherein saidcalibrating block comprises: a calculating circuit, arranged to estimatethe timing mismatch of said edge rotator according to said phase errorsamples; and an adjusting circuit, arranged to adjust said timing ofsaid edge rotator according to an output of said calculating circuit.17. The clock generating apparatus of claim 16, wherein said edgerotator comprises: a multiplexer, arranged to generate a multiplexeroutput by multiplexing said multiple phases of said second clockaccording to a control signal; and a controller, arranged to receivesaid multiplexer output and generate said control signal according tosaid multiplexer output.
 18. The clock generating apparatus of claim 17,wherein said output block further comprises: a toggle circuit, arrangedto receive said multiplexer output and generate said third clockaccording to said multiplexer output, wherein said third clock istoggled when said toggle circuit is triggered by said multiplexeroutput.
 19. The clock generating apparatus of claim 16, wherein saidphase error samples are derived from a reference phase and a variablephase corresponding to an output of said edge rotator.
 20. The clockgenerating apparatus of claim 19, wherein said reference phase isderived from a channel frequency command word (FCW) and a clockreference fed into a digital phase detector, and a fractional part of anFCW value is an inverse of a period of said edge rotator.
 21. The clockgenerating apparatus of claim 16 wherein said calculating circuitestimates said timing mismatch of said edge rotator by calculating adifference between a phase error sample of said phase error samples andeach of remaining phase error samples.
 22. The clock generatingapparatus of claim 16, wherein said adjusting circuit is arranged tohave accumulation functionality and follow a least mean square (LMS)algorithm to process said output of said calculating circuit.
 23. Theclock generating apparatus of claim 16, wherein a number of said phaseerror samples is equal to periodicity of said edge rotator.
 24. Theclock generating apparatus of claim 16, wherein said calibrating blockstochastically reduces said timing mismatch of said edge rotator.